MathematicsSyllabus Of Grade XII - MATHEMATICS (ME1207)
The Grade XII Mathematics syllabus is divided into six compulsory units. Separate marks are allotted to each unit and together they form a 3-hour examination of 100 marks.
Focus areas: relations and functions, algebra (matrices and determinants), differential and integral calculus, vectors and three-dimensional geometry, linear programming, and probability.
Total Marks: 100Time: 3 HoursAll six units are compulsory.
Instructions: This syllabus is divided into six units. Separate marks are given with each unit. The summary table below lists all units and marks, followed by detailed unit-wise content.
Relations and Functions: Types of relations - reflexive, symmetric, transitive and equivalence relations.
One to one and onto functions, composite functions and inverse of a function.
Binary operations.
Inverse Trigonometric Functions: Definition, range, domain, principal value branches.
Graphs of inverse trigonometric functions and elementary properties of inverse trigonometric functions.
Grade XII · Mathematics · Unit 2
Unit 2 · ALGEBRA (13 Marks)
13 Marks
Matrices: Concept, notation, order, equality, types of matrices, zero matrix, transpose of a matrix, symmetric and skew-symmetric matrices.
Addition, multiplication and scalar multiplication of matrices; simple properties of these operations.
Non-commutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restricted to square matrices of order 2).
Concept of elementary row and column operations.
Invertible matrices and proof of the uniqueness of inverse (if it exists). (All matrices have real entries.)
Determinants: Determinant of a square matrix (up to 3 × 3); properties of determinants, minors, cofactors and applications of determinants in finding the area of a triangle.
Adjoint and inverse of a square matrix.
Consistency, inconsistency and number of solutions of system of linear equations by examples.
Solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix.
Grade XII · Mathematics · Unit 3
Unit 3 · CALCULUS (44 Marks)
44 Marks
Continuity and Differentiability: Continuity and differentiability; derivative of composite functions; chain rule; derivatives of inverse trigonometric functions; derivative of implicit functions.
Concept of exponential and logarithmic functions and their derivatives; logarithmic differentiation.
Derivative of functions expressed in parametric form; second order derivatives.
Rolle’s and Lagrange’s Mean Value Theorems (without proof) and their geometric interpretations.
Applications of Derivatives: Rate of change; increasing and decreasing functions; tangents and normals; approximation; maxima and minima.
Simple problems that illustrate basic principles and understanding of the subject as well as real-life situations.
Integrals: Integration as inverse process of differentiation.
Integration of a variety of functions by substitution, by partial fractions and by parts; simple integrals to be evaluated.
Definite integrals as a limit of a sum; Fundamental Theorem of Calculus (without proof).
Basic properties of definite integrals and evaluation of definite integrals.
Applications of the Integrals: Applications in finding the area under simple curves, especially lines and circles/parabolas/ellipses (in standard form only).
Area between the above said curves (with clearly identifiable region).
Differential Equations: Definition, order and degree; general and particular solutions of a differential equation.
Formation of differential equations whose general solutions are given.
Solution of differential equations by method of separation of variables.
Homogeneous differential equations of first order and first degree.
Solutions of linear differential equations of the type: dy/dx + py = q where p and q are functions of x or constants; and dx/dy + px = q where p and q are functions of y or constants.
Grade XII · Mathematics · Unit 4
Unit 4 · VECTORS AND THREE-DIMENSIONAL GEOMETRY (17 Marks)
17 Marks
Vectors: Vectors and scalars; magnitude and direction of a vector.
Direction cosines and direction ratios of vectors.
Types of vectors: equal, unit, zero, parallel and collinear vectors.
Position vector of a point; negative of a vector; components of a vector.
Addition of vectors; multiplication of a vector by a scalar.
Position vector of a point dividing a line segment in a given ratio.
Scalar (dot) product of vectors and projection of a vector on a line.
Vector (cross) product of vectors.
Three-dimensional Geometry: Direction cosines and direction ratios of a line joining two points.
Cartesian and vector equation of a line; coplanar and skew lines; shortest distance between two lines.
Cartesian and vector equation of a plane.
Angle between (i) two lines, (ii) two planes, and (iii) a line and a plane.
Distance of a point from a plane.
Grade XII · Mathematics · Unit 5
Unit 5 · LINEAR PROGRAMMING (06 Marks)
6 Marks
Linear Programming: Introduction and definition of related terminology such as constraints, objective function and optimization.
Different types of linear programming (L.P.) problems.
Mathematical formulation of L.P. problems.
Graphical method of solution for problems in two variables.
Feasible and infeasible regions; feasible and infeasible solutions; optimal feasible solutions (up to three non-trivial constraints).
Grade XII · Mathematics · Unit 6
Unit 6 · PROBABILITY (10 Marks)
10 Marks
Multiplication theorem on probability.
Conditional probability and independent events.
Total probability theorem.
Bayes’ theorem.
Random variable and its probability distribution; mean and variance of a random variable.
Repeated independent (Bernoulli) trials and Binomial distribution.
